the ohio lottery has a game called pick 4 where a player pays $1 and picks a four - digit number. if the…

the ohio lottery has a game called pick 4 where a player pays $1 and picks a four - digit number. if the four numbers come up in the order you picked, then you win $2100. a) write the probability distribution for a player’s winnings. fill in the table below. for the computer to grade this one correctly make sure that your x values are from smallest to largest. b) what are your expected winnings? round final answer to 2 decimal places. put correct units in the second box.

the ohio lottery has a game called pick 4 where a player pays $1 and picks a four - digit number. if the four numbers come up in the order you picked, then you win $2100. a) write the probability distribution for a player’s winnings. fill in the table below. for the computer to grade this one correctly make sure that your x values are from smallest to largest. b) what are your expected winnings? round final answer to 2 decimal places. put correct units in the second box.

Answer

Explanation:

Step1: Determine possible winnings

The player pays $1. If they lose, their net - winnings (X=- 1). If they win, they get $2100 but they paid $1, so their net - winnings (X = 2100 - 1=2099).

Step2: Calculate probabilities

The total number of four - digit numbers (from (0000) to (9999)) is (n = 10\times10\times10\times10=10000). The probability of winning (P(X = 2099)=\frac{1}{10000}=0.0001). The probability of losing (P(X=-1)=1 - \frac{1}{10000}=\frac{9999}{10000}=0.9999).

Step3: Calculate expected value

The formula for the expected value (E(X)=\sum_{i}x_{i}P(x_{i})). So (E(X)=(-1)\times0.9999 + 2099\times0.0001). [ \begin{align*} E(X)&=- 0.9999+0.2099\ &=-0.79 \end{align*} ]

Answer:

a)

(X) (P(X))
(-1) (0.9999)
(2099) (0.0001)
b) (-0.79), dollars